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The structure of quantum spheres

Author: Albert Jeu-Liang Sheu
Journal: Proc. Amer. Math. Soc. 129 (2001), 3307-3311
MSC (2000): Primary 46L05; Secondary 17B37, 46L89, 47B35, 58B32, 81R50
Published electronically: April 2, 2001
MathSciNet review: 1845007
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We show that the C*-algebra $C\left(\mathbb{S} _{q}^{2n+1}\right)$ of a quantum sphere $\mathbb{S} _{q}^{2n+1}$, $q>1$, consists of continuous fields $\left\{f_{t}\right\}_{t\in\mathbb{T} }$ of operators $f_{t}$ in a C*-algebra $\mathcal{A}$, which contains the algebra $\mathcal{K}$ of compact operators with $\mathcal{A}/\mathcal{K}\cong C\left( \mathbb{S} _{q} ^{2n-1}\right) $, such that $\rho_{\ast}\left( f_{t}\right) $ is a constant function of $t\in\mathbb{T} $, where $\rho_{\ast}:\mathcal{A}\rightarrow \mathcal{A}/\mathcal{K}$ is the quotient map and $\mathbb{T} $ is the unit circle.

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Additional Information

Albert Jeu-Liang Sheu
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045

Keywords: Quantum spheres, quantum groups, groupoid C*-algebras, Toeplitz algebras
Received by editor(s): March 15, 2000
Published electronically: April 2, 2001
Additional Notes: The author was partially supported by NSF Grant DMS-9623008
Communicated by: David R. Larson
Article copyright: © Copyright 2001 American Mathematical Society

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